The champions kept the pressure on Manchester United ahead of the leaders' trip to Arsenal thanks to goals from Frank Lampard and Salomon Kalou that should never have been given.
Spurs were on course for their first victory at Stamford Bridge for 21 years after a spectacular first goal for the club from Sandro.
But goalkeeper Heurelho Gomes added another entry to his ever-increasing catalogue of howlers when he spilt Lampard's 35-yard strike, with assistant Mike Cairns wrongly ruling it had crossed the line.
The visitors, who needed to win to stay in the hunt for a top-four spot, looked like holding on for a draw that was no good to either side until substitute Kalou fired home in the 89th minute from an offside position, with Martin Yerby failing to raise his flag.
The watching Sir Alex Ferguson would not have been amused about the champions being gifted the most controversial of victories that put the pressure back on his United side.
The big question before the game was whether Carlo Ancelotti would put Chelsea's title hopes at risk by pairing Fernando Torres and Didier Drogba in attack.
Despite his last gamble of starting Torres in the Champions League defeat to United backfiring spectacularly, Ancelotti took a chance again.
He did play it safe with the system, retaining the 4-3-3 that had been key to the Blues still being in the championship reckoning.
But that meant Drogba playing on the right, a move that produced mixed results.
Torres' long-awaited first goal for the club had an obvious effect on the Spaniard's confidence but he never really had a sniff in the first half.
Drogba was also more subdued than of late but he almost opened the scoring with a blockbuster 35-yard free-kick that crashed off the crossbar.
Michael Essien - declared fit despite hobbling off against West Ham last week - and the in-form Florent Malouda also went close.
Otherwise, Spurs belied their recent form of one win in 10 and their miserable record at Stamford Bridge to give as good as they got, Roman Pavlyuchenko dragging wide after a Branislav Ivanovic slip.
But no one could have predicted the manner or scorer of their opening goal.
Sandro was bought as a defensive midfielder but there was nothing defensive about the touch and 30-yard half-volley that thundered through the fingertips of Petr Cech after 19 minutes.
The Brazilian instinctively ran to manager Harry Redknapp to celebrate only to receive a a monumental telling off.
Chelsea piled on the pressure, going too far at times, with Ivanovic booked and captain John Terry lucky to escape yellow on his 500th appearance for the club.
They should have levelled when Gomes tipped over Essien's header and the resulting corner saw Drogba flick the ball on for Torres, who stooped to nod over when he should have used his foot.
Sandro produced an excellent tackle on Lampard to deny him what looked a certain equaliser before all Tottenham's good work was undone on the stroke of half-time by Gomes' latest howler and an even bigger blunder by Cairns.
Gomes took no chances after the break when he parried a 25-yard shot from Drogba, who was then booked for foolishly refusing to give the ball to the referee.
With just under half and hour for his side to rescue his title bid, Ancelotti finally abandoned the Torres-Drogba experiment and restored Kalou to his attack.
Kalou's first touch was almost a goal as another Gomes blunder saw him punch Drogba's 40-yard free-kick straight at the striker, who had no time to react.
Chelsea screamed for a penalty when Younes Kaboul brought down Malouda but replays showed the tackle was clean.
The home side's attacks became increasingly frantic, while there was always the danger of being hit on the break.
Terry scuffed a disguised Drogba free-kick straight at Gomes before Chelsea's pressure finally told, with Drogba's shot deflecting to to Kalou to stab home.
Spurs pushed in vain for an equaliser and Gomes understandably had words with referee Andre Marriner as the players left the field.